I'm trying to teach myself how to quickly translate many different types of equations into VB, T-SQL and MDX code. Since I'm trying to build a skill, not just solve a single isolated problem, I'm try to figure this stuff out on my own as much as possible - but I'm stumped by the error function used in the calculation of the normal cumulative distribution function. In the equation I retrieved from the Wikipedia page "Normal Distribution," there is a $t$ symbol ($-t^2$, actually) which I can't find any references on.
Can anyone tell me what it means, and how to derive that value if it's not obvious? I can't figure out if it's a common calculus symbol or a measure used in statistics. Could it be one of the parameters used in integral differentiation, as mentioned at http://en.wikipedia.org/wiki/Parameter and http://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign ?
In addition, I've read that the CDF for a normal distribution is difficult to define precisely, so approximations based on things like Taylor Series and McLaurin Series are used. I want to figure out how to code such things on my own, if possible, but I was wondering if anyone had any thoughts on which method might be higher performing and which would yield greater precision.